REPRESENTATIONS OF SEMIGROUPS BY TRANSFORMATIONS AND THE CONGRUENCE LATTICE OF AN EVENTUALLY REGULAR SEMIGROUP
1996 ◽
Vol 06
(06)
◽
pp. 655-685
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Keyword(s):
On any eventually regular semigroup S, congruences ν, μL, μR, μ, K, KL, KR, ζ are introduced which are the greatest congruences over: nil-extensions (n.e.) of completely simple semigroups, n.e. of left groups, n.e. of right groups, n.e. of groups, n.e. of rectangular bands, n.e. of left zero semigroups, n.e. of right zero semigroups, nil-semigroups, respectively. Each of these congruences is induced by a certain representation of S which is defined on an arbitrary semigroup. These congruences play an important role in the study of lattices of varieties, pseudovarieties and existence varieties. The investigation also leads to eight complete congruences U, Tt, Tr, T, K, Kl, Kr, Z on the congruence lattice Con (S) of S.
1997 ◽
Vol 40
(3)
◽
pp. 457-472
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2004 ◽
Vol 69
(1)
◽
pp. 69-86
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Keyword(s):
1970 ◽
Vol 11
(4)
◽
pp. 417-420
1981 ◽
Vol 88
(3-4)
◽
pp. 293-313
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2013 ◽
Vol 94
(3)
◽
pp. 397-416
◽